AND THIN ELASTIC RODS. 369 



Had we supposed the curve to have retained always its statical form, the greatest value 



of — would have been only vS — . S. 

 dt •'a* 



— will also, during the motion, attain to more than its primitive value, 

 da* 



If p\bt = 7ir, -j^ will equal - 3.5 — nearly. This will be nearly the numerically maxi- 



(to Ot 



dPy 

 mum value of — — without regard to sign, and hence we see that a bent rod within the 

 dr 



breaking limit at the centre may be broken by the rebound after it is set free, as —, = -V 

 ° dsr a' 



only at starting, and an addition of ^th to the strain might determine fracture. 

 The following is a table of values of -r^(s = 0) for two successive values of t. 



do 



<p\})t = 140. 22', f\h't = 90«, -^ = 3.28 - . 



... =28°. 45l, ... =180, ...=3.34—. 



... = 430. 7'|, ... = 270, ... = 2.46 - . 



... =57". SO'i, ... =360, ...=1.43 — . 



... = 71". 52'|, ... = 450, 



... - 86". 15', ... = 540", 



... = 100«. 38', ... = 630", 



• •• ^ • • 



a 



I 

 a"' 



.65 



185 

 ^• 



S.5S 



That the maximum value of ~- is \/8 — ^ on the hypothesis of the deflected rod preserving, 



during the motion, the statical form due to the amount of displacement at its free end, may 

 be thus shewn. 



47—2 



